That this is so is not always clear; you have to read Eccles' entire story, and you have to read it carefully. A casual reading may leave readers with the impression that Eccles is a Darwinian; a careful reading discloses the affinity to Wallace. We don't have the space here to retell the story even synoptically, but we can convey its gist.
Eccles' starts spinning his narrative in the preface, where he informs us that he has ``been able to unfold the fascinating story of hominid evolution of the human brain" (, xi). But we soon see that there are two separate stories. The first spans the evolution of the mammalian brain from the primates to the emergence of homo sapiens (hs). The second story starts after the first ends, that is, after the brain of hs had arrived; it's the story of how we became -- to use Eccles' phrase -- human persons: incorporeal creatures able to control (and have experience through) human bodies.
The first story is in many ways told from the point of view of a detective recounting a solved case. Understanding the brain is made possible by inference from clues -- such as changes in posture and locomotion. For example, Eccles infers from the famous footprints found at the Laetoli beds in Northern Tanzania that Australopithecus (A) was erect and bipedal. He also goes on to speak of human-like relationships among A; this Eccles infers from hand-holding, which is in turn inferred from the fact that the footprints in question are side-by-side. That some of the footprints are superimposed one upon another implies, by Eccles' lights, that A was capable of both a fairly high level of concentration and fine motor control. Eccles makes similar types of inferences from such evidence throughout the book.
Eccles' evolutionary story includes his discussion of the development of fine motor control from early primates to hs in connection with expansion of motor cortical representation for the thumb and fingers. He tells us that it wasn't until these features of the brain evolved that tool-making could occur. The idea is that the raw physical ability was present, but there was inadequate brain power. This raises the obvious question: Why did these features of the brain evolve? In seeking an answer to this question one grasps the gist of Eccles' narrative, and one begins to see that Eccles and Darwin are worlds apart.
Eccles' answer to the question is that periods of stasis are punctuated by periods of rapid evolutionary change (speciation events), but with saltations and the creation of ``hopeful monsters." He cites Eldredge and Gould's  theory of punctuated equilibria for support of his saltatory view of evolution. The interesting thing about Eccles' view is that these changes have no selective value, at least initially. It is only later that they may have such an advantage. This phenomenon Eccles calls anticipatory evolution, which is similar to what Gould and Vrba  call exaptations. The basic idea is that features that may presently have a function that conveys a selective advantage for an organism may have arisen without a selective value or may have had a previously different function then it currently has. (See  for examples.) In a sense, the new function arises by serendipity, but Eccles seems to hold that there is indeed a reason for these changes, at least when it comes to the brain. So first we have bodies able to walk erect in bipedal fashion, and then comes the neural machinery able to control such bodies. And first we have a hand physically able to build tools, and then comes the neural machinery enabling the use of such a hand. And first we have mechanisms allowing for the production of an array of sounds, and then comes the neural stuff that can put these mechanisms to work in communicating. In all these cases, the prior mechanism comes in order to get ready for the subsequent neurological advance. The ultimate trick of this type is the core of Eccles' second story: the advent of dualist interactionism: the arrival of certain neural machinery in primates makes it possible, many years later, for persons, existing in the non-physical world of the mental, to interact with and control bodies. Such an exotic and teleological scheme certainly isn't Darwin's. It is Wallace's . As Eccles proudly confesses:
I believe that biological evolution is not simply chance and necessity. That could never have produced us with our values. I can sense with [Sherrington] that evolution may be the instrument of a Purpose, lifting it beyond chance and necessity at least in the transcendence that brought forth human creatures gifted with self-consciousness (, 116).